Experimental study of non-Darcy flow characteristics in permeable stones

[摘要] This study provides experimental evidence of Forchheimer flow and the transitionbetween different flow regimes from the perspective of the pore size ofpermeable stone. We first carry out seepage experiments on fourkinds of permeable stones with mesh sizes of 24, 46, 60 and 80, corresponding to mean particle sizes (50 % by weight)of 0.71, 0.36, 0.25 and 0.18 mm, respectively. The seepage experiments show that anobvious deviation from Darcy flow regime is visible. In addition, thecritical specific discharge corresponding to the transition between flow regimes(from pre-Darcy to post-Darcy) increases with increasing particlesize. When the “pseudo” hydraulic conductivity ( K , which is computed asthe ratio of the specific discharge q and the hydraulic gradient) increases withincreasing q , the flow regime is denoted pre-Darcy flow. After q increases to a certain value, the pseudo hydraulic conductivity beginsto decrease; this regime is called post-Darcy flow. In addition, we usethe mercury injection technique to measure the pore size distributions offour permeable stones with different particle sizes. The mercury injectioncurve is divided into three stages. The beginning and end segments of themercury injection curve are very gentle, with relatively small slopes, whilethe intermediate mercury injection curve is steep, indicating that the poresize in permeable stones is relatively uniform. The porosity decreases asthe mean particle sizes increases. The mean pore faithfully reflectsthe influences of the particle diameter, sorting degree and arrangement mode of theporous medium on seepage parameters. This study shows that the size of poresis an essential factor for determining the flow regime. In addition, theForchheimer coefficients are discussed. The coefficient A (whichis related to the linear term of the Forchheimer equation) is linearlyrelated to 1 / d 2 : A = 0.0025 1 / d 2 + 0.003 .The coefficient B (which is related to the quadratic term of the Forchheimerequation) is a quadratic function of 1 / d : B = 1.14 × 10 - 6 1 / d 2 - 1.26 × 10 - 6 1 / d . The porosity ( n ) can be usedto reveal the effects of the sorting degree and arrangement on the seepagecoefficients. A larger porosity leads to smaller coefficients A and B for the same particle size.

[学科分类] 妇产科学